Nonlinear Amplitude Equations and Soliton Excitations in Bose-Einstein Condensates

Radha Balakrishnan, Indubala I. Satija

Paulsamy Muruganandam, M. Lakshmanan

This chapter focuses on exploring localized excitations in the variable coefficient nonlinear Schrodinger (NLS) equation and its generalizations. The motivation comes from the fact that the NLS equation and its variants appear in several branches/topics of physics, including nonlinear optics and Bose-Einstein condensates (BECs). The chapter reviews critically the variety of matter wave solitons and their interactions in single- and multi-component Bose-Einstein condensates. It provides a brief overview of the mean Gross- Pitaevskii (GP) equation, derivation of the one-dimensional GP equation, and mapping of the 1D GP equation to the standard NLS equation. The chapter discusses matter wave single and multi bright and dark solitons of Bose– Einstein condensates with varying trap potentials and atomic interactions. It shows various solitons solutions of multi-component BECs described by the two coupled GP equations. In this case, the coupled GP equation has been mapped onto a two coupled NLS equation.

David L. Feder

Yuandong Xie

An improved nonlinear equation different from usual and an improved soliton solution of spinor Bose-Einstein condensates(BES)in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully.The width, peak and energy of soliton are also found.

Dániel Schumayer

Wei Fan, Bo Xiong, X Q Liu +2 more

Using an inverse scattering method, we find the exact bright and dark soliton solutions of the nonlinear Gross-Pitaevskii equation with external potentials. We also investigate the nonlinear excitation of a Bose-Einstein condensate under external fields. We reveal an efficient means of controlling solitons in a Bose-Einstein condensate for use in future experiments.